Question

x=2cos(3t+16) t is the time, x is the displacement.
Prove that v^2-ax is always constant, where v is the velocity and a is the acceleration.

Answer 1

Okay

Answer 2

What would I do next

Answer 3

work out \(\dot x\) and \(\ddot x\), ie \(v\) and \(a\)

then plug into the statement you have been asked to prove...

or, if you feel like it, go for \(v^2-ax \implies \dot x ^2 = \ddot x \, x \implies \dot x ^2 = \dot x \frac{d \dot x}{dx}x \implies \dot x = \frac{d \dot x}{dx}x\)

that's separable...so you have to prove that x is some constant multiple of v. this way, one differentiation does it.

Answer 4

That is great thanks